Chapter 10

Equilibrium constant, \(\mathrm{K}_{\mathrm{c}}\) for the reaction, \(\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NH}_{3(\mathrm{~g})}\); at \(500 \mathrm{~K}\) is \(0.061\) litre \({ }^{2} \mathrm{~mole}^{-2} .\) At a particular time, the analysis shows that composition of the reaction mixture is \(3.00\) mol litre \(^{-1} \cdot \mathrm{N}_{2}, 2.00\) mol litre \(^{-} \mathrm{H}_{2}\), and \(0.500\) mol litre \(^{-1} \mathrm{NH}_{3} .\) Is the reaction at equilibrium? If not, in which direction does the reaction tend to proceed to reach equilibrium?

Which of the following reactions will get affected by increase of pressure? Also mention, whether change will cause the reaction to go into the right or left direction? (i) \(\mathrm{CH}_{4(\mathrm{~g})}+2 \mathrm{~S}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{CS}_{2(\mathrm{~g})}+2 \mathrm{H}_{2} \mathrm{~S}_{(\mathrm{g})}\) (ii) \(\mathrm{CO}_{2(\mathrm{~g})}+\mathrm{C}_{(\mathrm{s})} \rightleftharpoons 2 \mathrm{CO}_{(\mathrm{g})}\) (iii) \(4 \mathrm{NH}_{3(\mathrm{~g})}+5 \mathrm{O}_{2(\mathrm{~g})} \rightleftharpoons 4 \mathrm{NO}_{(\mathrm{g})}+6 \mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})}\) (iv) \(\mathrm{C}_{2} \mathrm{H}_{4(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6(\mathrm{~g})}\)

In which case does the reaction go farthest to completion : \(K=1 ; K=10^{10} ; K=10^{-10}\) and why?

Nitric oxide reacts with bromine and gives nitrosyl-bromide as per reaction given below: $$ 2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{Br}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NOBr}_{(\mathrm{g})} $$ When \(0.087\) mole of \(\mathrm{NO}\) and \(0.0437\) mole of \(\mathrm{Br}_{2}\) are mixed is a closed container at constant temperature, \(0.0518\) mole of NOBr is obtained at equilibrium. Calculate equilibrium amount of nitric oxide and bromine.

The first order diffraction of \(X\) -rays from a certain set of crystal planes oceurs at an angle of \(11.8^{\circ}\) from the planes. If the planes are \(0.281 \mathrm{~nm}\) apart, what is the wavelength of \(X\) -rays?

If a mixture of 3 moles of \(\mathrm{H}_{2}\) and one mole of \(\mathrm{N}_{2}\) is completely converted into \(\mathrm{NH}_{3}\). What would be the ratio of the initial and final volume at same temperature and pressure?

The ester, ethyl acetate is formed by the reaction between ethanol and acetic acid and equilibrium is represented as : \(\mathrm{CH}_{3} \mathrm{COOH}_{(\mathrm{l})}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}_{(\mathrm{l})} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5(\mathrm{aq})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})}\) (a) Write the concentration ratio (reaction quotient), \(Q_{\mathrm{e}}\), for this reaction. Note that water is not in excess and is not a solvent in this reaction. (b) At \(293 \mathrm{~K}\), if one starts with \(1.00\) mole of acetic acid and \(0.180\) of ethanol, there is \(0.171\) mole of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant. (c) Starting with \(0.500\) mole of ethanol and \(1.000\) mole of acetic acid and maintaining it at \(293 \mathrm{~K}, 0.214\) mole of ethyl acetate is found after some time. Has equilibrium been reached?

For the gaseous reaction; \(2 \mathrm{NO}_{2} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}\), calculate \(\Delta \mathrm{G}^{\circ}\) and \(K_{\mathrm{p}}\) for the reaction at \(25^{\circ} \mathrm{C}\). Given \(\mathrm{G}_{j}^{\circ} \mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{G}_{f}^{\circ} \mathrm{NO}_{2}\) are \(97.82\) and \(51.30\) \(\mathrm{kJ}\) respectively. Also calculate \(\Delta \mathrm{G}^{\circ}\) and \(K_{\mathrm{p}}\) for reverse reaction.

\(\Delta G^{\circ}\) for \(\frac{1}{2} \mathrm{~N}_{2}+\frac{3}{2} \mathrm{H}_{2} \rightleftharpoons \mathrm{NH}_{3}\) is \(-16.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at \(25^{\circ} \mathrm{C}\). Find out \(K_{\mathrm{p}}\) for the reaction. Also report \(K_{\mathrm{p}}\) and \(\Delta G^{\circ}\) for: $$ \mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3} \quad \text { at } 25^{\circ} \mathrm{C} $$

\(K_{\mathrm{c}}\) for the reaction; \(A+B \Longrightarrow P+Q\), is \(2.0 \times 10^{-2}\) at \(25^{\circ} \mathrm{C}\) and it is \(2.0 \times 10^{-1}\) at \(50^{\circ} \mathrm{C}\). Predict whether the forward reaction is exothermic or endothermic.